Suppose that V is finite dimensional and S,T belong to L(V). Prove that ST=1 if and only if TS=1.

Could someone get me started on this please? Thanks for any help.

I think what you need is: if V is a fin. dimensional v.s. then a linear transformation is 1-1 iff it is onto, and thus:
A lin. transf. in a fin. dim. v.s. is invertible iff it is 1-1.
Finally, for any two functions :

I think what you need is: if V is a fin. dimensional v.s. then a linear transformation is 1-1 iff it is onto, and thus:
A lin. transf. in a fin. dim. v.s. is invertible iff it is 1-1.
Finally, for any two functions :